If there was a <3 button here, I would use it for this post.
There are really no more actual "dual purpose" breeds - largely because we don't use chickens the way we used to. Chicken wasn't generally some huge, meaty thing that you roasted in the oven. It was something you fried (young cockerel) or stewed (older hens), slow-cooked in wine (mature roosters) and the idea was to get a balance between keeping decent egg-laying ability and not feeding strapping huge hens all winter and having a decent carcass to show for your trouble, because Me-Maw served up ALL the birds eventually;
... it was just a question of when they were best served. "Dual purpose" breeds, back when Granny was using hard-earned money and grain that HAD to feed the family in some way, were those that were economical to keep past "Yup, that one's a boy" and fatten instead of frying the little things up every Sunday after they'd revealed themselves.
~BUT~ One year is a chicken generation. If a breed was known for this in 1950, but since than has been bred for show (form and feather, production and maturity rate unimportant) or for backyards (color and egg-laying ability), well, that was 77 generations ago, or, in human terms; What were YOUR ancestors up to around the year 498 and how does it show in you now?
If you want to do like Grandma did, yes, separate the birds. You want to mark the FIRST little clucker to show himself to be a rooster and keep THAT one - NOT the one who snuck by with the pullets until they started to lay. The first way you're breeding for faster maturity, like Nanny wanted, the second, you are breeding for slow growth and late egg laying. But you're not really going to fatten them, so much as keep an eye on who's growing the fastest (again, that's the boy you want) and keeping them from harassing the ladies. Past that, raise them for the recipe you want. It will NOT be roast chicken ... or at least not like you're used to.
You do that for 5 - 10 years, selecting the meatiest rooster from the first handful to get little red combs and give you the side-eye, and breeding him to the heaviest 5 of the first 10 pullets to lay an egg and you'll be well on your way to having a bird your ancestors would recognize as dual-purpose